In the capital, a granary, for the food bonus. On 80% of maps this makes for fastest expansion. In the first few cities, barracks are often the first choice for an early war when I get to 4 to 6 cities. After the initial ring of cities, the cheapest culture building, temples or libraries, especially in captured cities.
Later, courthouses and marketplaces get high priority, depending on how far the city is from the capital. Courthouses to reduce corruption, marketplaces to increase gold and happiness. For coastal cities that have no food squares, harbors. Also harbors if needed to hook up a luxury into the empire network (island city).
+ Bill